What is 4ln(8)-4ln(4) ?

The solution to 4ln(8)-4ln(4) is 4ln(2)

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simplify 4ln(8)-4ln(4)

simplify

4 ln (8) - 4 ln (4)

4 ln (2)

Decimal Notation

2.77258 \dots

Solution steps

4 ln (8) - 4 ln (4)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (8) = ln (8^{4})

= ln (8^{4}) - 4 ln (4)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (4) = ln (4^{4})

= ln (8^{4}) - ln (4^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (8^{4}) - ln (4^{4}) = ln (\frac{8 ^{4}}{4 ^{4}})

= ln (\frac{8 ^{4}}{4 ^{4}})

\frac{8 ^{4}}{4 ^{4}} = 16

= ln (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= ln (2^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{4}) = 4 ln (2)

= 4 ln (2)

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